LC Method Scaling, Part I: Isocratic Separations

What kind of adjustments need to be made when scaling an isocratic method?

Today we are often confronted with many different types of liquid chromatography (LC) methods. These may use conventional 250 or 150 mm × 4.6 mm, 150 mm × 2.1 mm, 50 mm × 2.1 mm, and many other column configurations packed with particles generally ranging from <2 μm to 5 μm, and sometimes even 10 μm in diameter. One of the challenges this variety presents is transferring a method from one column configuration to another and still obtaining the same resulting separation. For example, you may use an ultrahigh-pressure LC (UHPLC) system to develop methods quickly in your research and development (R&D) laboratory, but want to transfer it to a conventional LC system for routine use. Or your conventional method with ultraviolet detection (LC–UV) may need to be transferred to an LC system with mass spectrometry detection (LC–MS). Alternatively, you may want to adjust a pharmacopeial method to use a different column configuration. In many of these cases, the method must be moved from one column size to another, yet maintain the same separation. The conversion is not difficult, but you do have to be careful to make the appropriate adjustments. Isocratic separations, in which the mobile-phase concentration is constant, are simpler to convert than gradient methods, where special care has to be taken to avoid inadvertent chromatographic changes. This month's "LC Troubleshooting" discussion focuses on isocratic separations, and next month we'll look at gradients.

Resolution Is the Key

Equivalent separations require that the resolution stays the same when conditions are changed. In the method development classes we teach, we use what is often referred to as the "fundamental resolution equation" as a guide for the method development process. We can use this same equation to guide us in method conversion:

where Rs is resolution, N is the column plate number, α is the separation factor, and k is the retention factor. The first caveat is that the chemistry of the system cannot change when a change in the column or other conditions changes. This means that the mobile phase must remain the same, as well as the column temperature and column chemistry. With today's columns, it usually is valid to assume that the same brand name description of a column (for example, ACE C18 [Advanced Chromatography Technologies Ltd.) will have the same column chemistry, no matter what the particle size is (2, 3, 5 μm, and so forth). You'll recall that the retention factor is defined as:

where tR is the retention time of a solute and t0 is the column dead time (retention time of an unretained peak). If we keep the chemistry of the system constant, the retention time relative to the dead time should stay constant, so k will remain unchanged. Any change in retention because of a change in column length, diameter, or flow rate will have a proportional change for tR and t0, so k will stay constant in this case as well. For example, doubling the flow rate will halve tR and t0, and k will be unchanged.

The separation factor α is simply the ratio of k values for two adjacent peaks, k1 and k2:

So if we keep k constant, as discussed above, α will be unchanged. If k and α are kept constant, to keep Rs constant (equation 1), all that remains is to make sure that the column plate number stays constant.

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